Abstract
This paper is devoted to the construction and study of the stability and convergence of a numerical method for solving the problem of three-phase non-isothermal fluid flow in porous media, taking into account capillary forces, which was carried out within the framework of the grant project No. AP08053189 provided by the Ministry of Education and Science of the Republic of Kazakhstan. The model under consideration describes the processes occurring in oil reservoirs during the production of heavy oil by the method of thermal steam stimulation of the reservoir. The formulation of the differential problem is based on the introduction of a change of variables called global pressure, which makes it possible to exclude the capillary pressure gradient from the pressure equation. For the numerical solution, a numerical scheme was constructed. An a priori estimate in the energy norm is obtained, which expresses the stability of the constructed scheme with respect to the initial data and the right-hand sides of the equations. The theorem on the convergence of the solution of a numerical scheme to the solution of a differential problem is presented.